1. Technical Field
The present invention relates to a flexural vibration element which vibrates in a flexural vibration mode, and various electronic components including the flexural vibration element, such as a vibrator, a resonator, an oscillator gyro, and various sensors.
2. Related Art
As a piezoelectric vibration element in a flexural vibration mode, such a tuning fork type piezoelectric vibration element has been widely used that a pair of vibrating arms is extended in parallel from a base part and the vibrating arms vibrate closer to or away from each other in a horizontal direction. Vibration energy loss generated when the vibrating arms perform flexural vibration causes degradation of performance of a vibrator such as increase of a CI value and decrease of a Q value. Therefore, various ways for preventing or reducing the vibration energy loss has been contrived.
JP-A-2002-261575 as a first example and JP-A-2004-260718 as a second example disclose a tuning fork type quartz crystal vibration element in which cuts or cut-grooves having a predetermined depth are formed at both side parts of a base part from which vibrating arms extend. In the quartz crystal vibration element, even in a case where the vibrating arms generate vibration including a vertical component, vibration leak from the base part is suppressed by the cuts or the cut-grooves so as to improve a vibration energy trapping effect and prevent variation of CI values among vibration elements.
Not only such the mechanical loss but also vibration energy loss is generated by heat conduction due to temperature difference between a compressive part and a tensile part, which receives tensile stress, of the vibrating arms which perform flexural vibration. Decrease of the Q value caused by the heat conduction is called a thermoelastic loss. In order to prevent or suppress the decrease of the Q value due to the thermalelastic loss, Japanese Patent Application No. 63-110151 as a third example proposes a tuning fork type vibrator, in which a groove or a hole is formed on a centerline of a vibrating arm (vibrating beam) having a rectangular section.
The third example describes that the Q value becomes minimum when a relaxation frequency fm is expressed as fm=½πτ (here, π denotes circle ratio, and τ denotes relaxation time) in a vibrator in a flexural vibration mode. This is based on a relational equation, which is well known, of distortion and stress in a case of internal friction, which is generally caused by temperature difference, of a solid substance. A relationship between a Q value and a frequency is generally expressed as a curve F of FIG. 5 (refer to, for example, C. Zener et al., “Internal Friction in Solids III. Experimental Demonstration of Thermoelastic Internal Friction”, Physical Review, Volume 53, pp. 100-101 (January 1938)). Referring to FIG. 5, the Q value becomes a minimum value Q0 at a relaxation frequency f0 (=½πτ).
Here, it is also known that the relaxation frequency f0 can be obtained from the following formula.f0=πk/(2ρCp a2)  (1)Here, π denotes circle ratio, k denotes a thermal capacity of a vibration part (flexural vibration part), and a denotes a width of the vibration part (flexural vibration part) in a vibrating direction (flexural vibrating direction).
On the other hand, as a flexural vibrator other than that of a tuning fork type, JP-A-2006-345519 as a fourth example discloses a resonator in which two parallel vibrating arms are coupled to each other by a connecting part and a central arm is extended between the vibrating arms from the connecting part. The resonator is composed of a single-component vibration element made of quartz crystal. In the resonator, at least one groove is formed on at least one of a front surface and a rear surface of the vibrating arms so as to make an excitation electric field even and regionally-strong, reducing energy consumption and limiting a CI value. Further, the groove of the vibrating arms is extended to the connecting part, at which mechanical stress is maximum, to extract an electric field in this region, increasing a vibration coupling effect of the vibrating arms.
Vibration elements vibrating in the flexural vibration mode include a vibration element of an electrostatic driving type using electrostatic force and a vibration element of a magnetic driving type using magnetism as well as the vibration element of the piezoelectric driving type described above. JP-A-5-312576 as a fifth example discloses an angular velocity sensor as a vibration element of the electrostatic driving type. In the angular velocity sensor, a first vibrating body composed of a square frame part is supported by a first supporting beam so as to be able to vibrate in X-axis direction, and a second vibrating body having a square plain plate shape is supported by a second supporting beam so as to be able to vibrate in Y-axis direction, on a substrate made of a silicon material. The first supporting beam bends due to electrostatic force which is generated between a fixed conductive part provided on an end part of the substrate and a movable conductive part provided on an end part of the first vibrating body. Thus the first vibrating body vibrates in the X-axis direction. JP-A-2001-183140 as a sixth example discloses another angular velocity sensor as another vibration element of the electrostatic driving type. This angular velocity sensor is composed of a sensor body made of a silicon wafer and a glass substrate opposed to the sensor body. The sensor body has plummets held in an inside of a vibration frame, which is supported in a fixed frame by a driving beam, by multiple beams. The sensor body and the plummets vibrate due to electrostatic force generated between parallel plain plate electrodes provided on the sensor body and the glass substrate.
Further, JP-B-43-1194 as a seventh example discloses a vibrating body structure as a vibration element of the magnetic driving type. In the vibrating body structure, a vibrating body made of a constant modulus material is fixed and supported on an external fixing pedestal at its supporting part at one end thereof. A spring part branched from a connecting part between the vibrating body and the pedestal is driven and vibrated by magnet fixed to a free end of the spring part and by an electromagnetic coil fixed to a base. JP-A-10-19577 as an eighth example discloses an angular velocity sensor as another vibration element of the magnetic driving type. In the angular velocity sensor, a thin film magnet is disposed on a thin film vibrating plate which is composed of a silicon substrate and is supported as a cantilever beam. The thin film vibrating plate is vibrated in a thickness direction by an effect of electromagnetic force generated by applying alternating current to a conductor or an electromagnetic coil provided outside the thin film vibrating plate.
However, as far as the inventor knows, almost only the third example studies an influence of the above-mentioned thermoelastic loss given to the piezoelectric vibration element in a flexural vibration mode, among related arts. The inventor studied an influence of thermoelastic loss, caused by flexural vibration of vibrating arms, on performances of the vibrating arms in a piezoelectric vibration element having such a structure that one central supporting arm was extended between the two vibrating arms from a connecting part as illustrated in the fourth example.
Referring to FIG. 6, this piezoelectric vibration element 1 includes two vibrating arms 3 and 4 extending from a connecting part 2 in parallel. Between the vibrating arms 3 and 4, one central supporting arm 5 extends in parallel with the arms 3 and 4 at equal distance from the arms 3 and 4. A linear groove 6 is formed on each of a front surface and a rear surface of the vibrating arm 3 and a linear groove 7 is formed on each of a front surface and a rear surface of the vibrating arm 4. The piezoelectric vibration element 1 is fixed and held on a package or the like, which is not shown, at an end of the central supporting arm 5, that is, at an end part opposite to the connecting part 2. When predetermined voltage is applied to an excitation electrode, which is not shown, in this state, the vibrating arms 3 and 4 perform flexural vibration in a direction closer to or away from each other as shown by imaginary lines and arrows in the drawing.
Because of this flexural vibration, mechanical distortion occurred in the connecting part 2 along a width direction of the vibrating arms 3 and 4, concretely, at a region 8 between a connecting portion of the connecting part 2 with the vibrating arm 3 and a connecting portion of the same with the central supporting arm 5, and at a region 9 between a connecting portion of the connecting part 2 with the vibrating arm 4 and the connecting portion of the same with the central supporting arm 5. This distortion was observed as relatively large temperature gradients between a part 10 at a vibrating arm side of the region 8 and a part 12 opposed to the part 10 and between a part 11 at the vibrating arm side of the region 9 and a part 13 opposed to the 11. When the vibrating arms 3 and 4 bent closer to each other, compressive stress acted on the parts 10 and 11 at the vibrating arm side respectively in the regions 8 and 9 so as to increase the temperatures of the parts 10 and 11, and tensile stress acted on the parts 12 and 13, which were respectively opposed to the parts 10 and 11, so as to decrease the temperatures of the parts 12 and 13. In an opposite manner, when the vibrating arms 3 and 4 bent away from each other, tensile stress acted on the parts 10 and 11 at the vibrating arm side respectively in the regions 8 and 9 so as to decrease the temperatures of the parts 10 and 11, and compressive stress acted on the parts 12 and 13, which were respectively opposed to the parts 10 and 11, so as to increase the temperatures of the parts 12 and 13.
Because of the temperature gradients, heat conduction occurs in the connecting part 2 between the part 10 at the vibrating arm side of the region 8 and the part 12 opposed to the part 10, and between the part 11 at the vibrating arm side of the region 9 and the part 13 opposed to the part 11. The temperature gradients in opposite directions to each other occur respectively at the vibrating arm side and at the opposite side of the vibrating arm side while corresponding to the flexural vibration of the vibrating arms, generating heat conductions in opposite directions to each other. Because of the heat conductions, part of vibration energy of the vibrating arms 3 and 4 is constantly lost during their vibration as the thermoelastic loss. As a result, a Q value of the vibration element is degraded, making hard to achieve desired high-performance of the vibration element.